// Copyright 2010 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// package math -- go2cs converted at 2022 March 13 05:42:01 UTC
// import "math" ==> using math = go.math_package
// Original source: C:\Program Files\Go\src\math\jn.go
namespace go;

public static partial class math_package {

/*
    Bessel function of the first and second kinds of order n.
*/

// The original C code and the long comment below are
// from FreeBSD's /usr/src/lib/msun/src/e_jn.c and
// came with this notice. The go code is a simplified
// version of the original C.
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunPro, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
//
// __ieee754_jn(n, x), __ieee754_yn(n, x)
// floating point Bessel's function of the 1st and 2nd kind
// of order n
//
// Special cases:
//      y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
//      y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
// Note 2. About jn(n,x), yn(n,x)
//      For n=0, j0(x) is called,
//      for n=1, j1(x) is called,
//      for n<x, forward recursion is used starting
//      from values of j0(x) and j1(x).
//      for n>x, a continued fraction approximation to
//      j(n,x)/j(n-1,x) is evaluated and then backward
//      recursion is used starting from a supposed value
//      for j(n,x). The resulting value of j(0,x) is
//      compared with the actual value to correct the
//      supposed value of j(n,x).
//
//      yn(n,x) is similar in all respects, except
//      that forward recursion is used for all
//      values of n>1.

// Jn returns the order-n Bessel function of the first kind.
//
// Special cases are:
//    Jn(n, ±Inf) = 0
//    Jn(n, NaN) = NaN
public static double Jn(nint n, double x) {
    const float TwoM29 = 1.0F / (1 << 29); // 2**-29 0x3e10000000000000
    const nint Two302 = 1 << 302; // 2**302 0x52D0000000000000 
    // special cases

    if (IsNaN(x)) 
        return x;
    else if (IsInf(x, 0)) 
        return 0;
    // J(-n, x) = (-1)**n * J(n, x), J(n, -x) = (-1)**n * J(n, x)
    // Thus, J(-n, x) = J(n, -x)

    if (n == 0) {
        return J0(x);
    }
    if (x == 0) {
        return 0;
    }
    if (n < 0) {
        (n, x) = (-n, -x);
    }
    if (n == 1) {
        return J1(x);
    }
    var sign = false;
    if (x < 0) {
        x = -x;
        if (n & 1 == 1) {
            sign = true; // odd n and negative x
        }
    }
    double b = default;
    if (float64(n) <= x) { 
        // Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x)
        if (x >= Two302) { // x > 2**302

            // (x >> n**2)
            //          Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
            //          Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
            //          Let s=sin(x), c=cos(x),
            //              xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
            //
            //                 n    sin(xn)*sqt2    cos(xn)*sqt2
            //              ----------------------------------
            //                 0     s-c             c+s
            //                 1    -s-c            -c+s
            //                 2    -s+c            -c-s
            //                 3     s+c             c-s

            double temp = default;
            {
                var (s, c) = Sincos(x);

                switch (n & 3) {
                    case 0: 
                        temp = c + s;
                        break;
                    case 1: 
                        temp = -c + s;
                        break;
                    case 2: 
                        temp = -c - s;
                        break;
                    case 3: 
                        temp = c - s;
                        break;
                }
            }
            b = (1 / SqrtPi) * temp / Sqrt(x);
        }
        else
 {
            b = J1(x);
            {
                nint i__prev1 = i;
                var a__prev1 = a;

                for (nint i = 1;
                var a = J0(x); i < n; i++) {
                    (a, b) = (b, b * (float64(i + i) / x) - a);
                }

                i = i__prev1;
                a = a__prev1;
            }
        }
    else
    } {
        if (x < TwoM29) { // x < 2**-29
            // x is tiny, return the first Taylor expansion of J(n,x)
            // J(n,x) = 1/n!*(x/2)**n  - ...

            if (n > 33) { // underflow
                b = 0;
            }
            else
 {
                temp = x * 0.5F;
                b = temp;
                a = 1.0F;
                {
                    nint i__prev1 = i;

                    for (i = 2; i <= n; i++) {
                        a *= float64(i); // a = n!
                        b *= temp; // b = (x/2)**n
                    }

                    i = i__prev1;
                }
                b /= a;
            }
        else
        } { 
            // use backward recurrence
            //                      x      x**2      x**2
            //  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
            //                      2n  - 2(n+1) - 2(n+2)
            //
            //                      1      1        1
            //  (for large x)   =  ----  ------   ------   .....
            //                      2n   2(n+1)   2(n+2)
            //                      -- - ------ - ------ -
            //                       x     x         x
            //
            // Let w = 2n/x and h=2/x, then the above quotient
            // is equal to the continued fraction:
            //                  1
            //      = -----------------------
            //                     1
            //         w - -----------------
            //                        1
            //              w+h - ---------
            //                     w+2h - ...
            //
            // To determine how many terms needed, let
            // Q(0) = w, Q(1) = w(w+h) - 1,
            // Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
            // When Q(k) > 1e4    good for single
            // When Q(k) > 1e9    good for double
            // When Q(k) > 1e17    good for quadruple

            // determine k
            var w = float64(n + n) / x;
            nint h = 2 / x;
            var q0 = w;
            var z = w + h;
            var q1 = w * z - 1;
            nint k = 1;
            while (q1 < 1e9F) {
                k++;
                z += h;
                (q0, q1) = (q1, z * q1 - q0);
            }
            var m = n + n;
            float t = 0.0F;
            {
                nint i__prev1 = i;

                i = 2 * (n + k);

                while (i >= m) {
                    t = 1 / (float64(i) / x - t);
                    i -= 2;
                }

                i = i__prev1;
            }
            a = t;
            b = 1; 
            //  estimate log((2/x)**n*n!) = n*log(2/x)+n*ln(n)
            //  Hence, if n*(log(2n/x)) > ...
            //  single 8.8722839355e+01
            //  double 7.09782712893383973096e+02
            //  long double 1.1356523406294143949491931077970765006170e+04
            //  then recurrent value may overflow and the result is
            //  likely underflow to zero

            var tmp = float64(n);
            nint v = 2 / x;
            tmp = tmp * Log(Abs(v * tmp));
            if (tmp < 7.09782712893383973096e+02F) {
                {
                    nint i__prev1 = i;

                    for (i = n - 1; i > 0; i--) {
                        var di = float64(i + i);
                        (a, b) = (b, b * di / x - a);
                    }
            else


                    i = i__prev1;
                }
            } {
                {
                    nint i__prev1 = i;

                    for (i = n - 1; i > 0; i--) {
                        di = float64(i + i);
                        (a, b) = (b, b * di / x - a);                        if (b > 1e100F) {
                            a /= b;
                            t /= b;
                            b = 1;
                        }
                    }

                    i = i__prev1;
                }
            }
            b = t * J0(x) / b;
        }
    }
    if (sign) {
        return -b;
    }
    return b;
}

// Yn returns the order-n Bessel function of the second kind.
//
// Special cases are:
//    Yn(n, +Inf) = 0
//    Yn(n ≥ 0, 0) = -Inf
//    Yn(n < 0, 0) = +Inf if n is odd, -Inf if n is even
//    Yn(n, x < 0) = NaN
//    Yn(n, NaN) = NaN
public static double Yn(nint n, double x) {
    const nint Two302 = 1 << 302; // 2**302 0x52D0000000000000
    // special cases
 // 2**302 0x52D0000000000000
    // special cases

    if (x < 0 || IsNaN(x)) 
        return NaN();
    else if (IsInf(x, 1)) 
        return 0;
        if (n == 0) {
        return Y0(x);
    }
    if (x == 0) {
        if (n < 0 && n & 1 == 1) {
            return Inf(1);
        }
        return Inf(-1);
    }
    var sign = false;
    if (n < 0) {
        n = -n;
        if (n & 1 == 1) {
            sign = true; // sign true if n < 0 && |n| odd
        }
    }
    if (n == 1) {
        if (sign) {
            return -Y1(x);
        }
        return Y1(x);
    }
    double b = default;
    if (x >= Two302) { // x > 2**302
        // (x >> n**2)
        //        Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
        //        Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
        //        Let s=sin(x), c=cos(x),
        //        xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
        //
        //           n    sin(xn)*sqt2    cos(xn)*sqt2
        //        ----------------------------------
        //           0     s-c         c+s
        //           1    -s-c         -c+s
        //           2    -s+c        -c-s
        //           3     s+c         c-s

        double temp = default;
        {
            var (s, c) = Sincos(x);

            switch (n & 3) {
                case 0: 
                    temp = s - c;
                    break;
                case 1: 
                    temp = -s - c;
                    break;
                case 2: 
                    temp = -s + c;
                    break;
                case 3: 
                    temp = s + c;
                    break;
            }
        }
        b = (1 / SqrtPi) * temp / Sqrt(x);
    }
    else
 {
        var a = Y0(x);
        b = Y1(x); 
        // quit if b is -inf
        for (nint i = 1; i < n && !IsInf(b, -1); i++) {
            (a, b) = (b, (float64(i + i) / x) * b - a);
        }
    }
    if (sign) {
        return -b;
    }
    return b;
}

} // end math_package
